As for the pressurant gas dissolving into the propellant in non-PMD tanks, I don't know enough about that. I imagine the solubility of He (it is usually helium) in these propellants is either accounted for, or negligible.
Edit: P.S. Software engineering is mostly foreign to me and much of HN content is over my head, but I like he level of discourse here. So, when a topic came up that I could actually contribute to, I jumped.
This is because Helium has very weak intermolecular forces due to its electronic symmetry. For that same reason, it's also as close to an ideal gas, giving you the most pressure/volume bang for your mass buck (only hydrogen is better, and that's bad for oxidizer tanks for obvious reasons).
But this also limits the ability to cryogenically condense helium, which would improve storage density. But you really don't need much in turbopump fed engines.
When you say "metal bladder/diaphragm" is that a sliding wall with propellant on one side and pressurant on the other? (I can't imagine how the seals in that would work.) Or do you mean the metal actually deforms in place?
For an excellent deep dive into the systems, operations, and functions of the Saturn V, get a copy of "How Apollo Flew to the Moon" by W. David Woods.
So the short answer here is: no, it won't.
But mostly chosen pressurant which is not dissolves, or used some type of separating membrane (or piston), for example, in Soviet space stations used https://en.wikipedia.org/wiki/Metal_bellows
No expert though :)